Question

integrate the function [sin^{-1}x]/[√(1 - x²)] .dx

Answer 1

HELLO DEAR,

given function is $\bold{\int{\frac{sin^{-1}x}{\sqrt{1 - x^2}}}\,dx}$

let sin^{-1}x = t $\bold{\Rightarrow dt/dx = 1/\sqrt{1 - x^2}}$
$\bold{\Rightarrow dx = \sqrt{1 - x^2}\,dt}$

now, $\bold{\int{\frac{sin^{-1}x}{\sqrt{1 - x^2}}*\sqrt{1 - x^2}}\,dt}$

$\bold{\int{t}\,dt}$

$\bold{t^2/2 + C}$

$\bold{(sin^{-1}x)^2/2 + C}$

where, C is the arbitrary constant.

I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Hope it will help you!!